Application of Proper Orthogonal Decomposition (POD) to inverse problems in saturated groundwater flow |
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| Authors: | Corey Winton Jackie Pettway |
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| Institution: | a 3909 Halls Ferry Road, Vicksburg, MS 39180, United States
b Department of Mathematics, Box 8025, North Carolina State University, Raleigh, NC 27695-8205, United States |
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| Abstract: | We develop a new Proper Orthogonal Decomposition (POD) reduced order model for saturated groundwater flow, and apply that model to an inverse problem for the hydraulic conductivity field. We use sensitivities as the POD basis. We compare the output when the optimizer uses the reduced order model against results obtained with a full PDE based model. The solutions generated using the POD reduced model are comparable in residual norm to the solutions formed using only the full-scale model. The material parameters are similarly comparable. The time to solution when using the reduced model is reduced by at least an order of magnitude, as are the number of calls to the full model. |
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| Keywords: | Proper Orthogonal Decomposition Optimization Parameter estimation Inverse problem Saturated groundwater flow |
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